feat(billing): embed Stripe Payment Element in onboarding (#21759)

## What & why

Replaces the hosted Stripe Checkout redirect on the onboarding "Choose
your plan" step (credit-card trial) with an inline Stripe **Payment
Element**, so users never leave the app to enter card details.

## How it works

- **Frontend:** a deferred `<Elements mode="setup">` renders the Payment
Element, themed via the Appearance API. On Continue: `elements.submit()`
→ `checkoutSession` mutation creates the trialing subscription
server-side and returns its pending SetupIntent `clientSecret` →
`stripe.confirmSetup()` confirms the card (handling 3DS) → redirect to
the existing `/plan-required/payment-success`.
- **Backend:** new `BILLING_STRIPE_PUBLISHABLE_KEY` config var exposed
via `/client-config`; the card path creates the subscription with
`payment_behavior: default_incomplete` + a free trial (so Stripe
attaches a `pending_setup_intent`) and returns its client secret. The
hosted-Checkout code path is removed.
- The **no-credit-card** trial path is unchanged.
- Billing address collection is **disabled** in the Payment Element to
reduce friction; `automatic_tax` is correspondingly disabled (tax needs
an address — collect it later, e.g. at conversion / via the billing
portal).

## Required before this works
1. Set `BILLING_STRIPE_PUBLISHABLE_KEY` (`pk_…`) on the server (infra
change pending).
2. Run `nx run twenty-front:graphql:generate --configuration=metadata`
against a server exposing the updated schema (see inline note on the
hand-authored document).
3. Verify in Stripe test mode: happy path, 3DS (`4000 0025 0000 3155`),
a decline.

## Verified
typecheck (front + server), oxlint + oxfmt clean,
`client-config.service.spec` passing. Not run here: the app end-to-end /
Stripe test mode and `graphql:generate` (no server/DB in the dev
container).

I've left self-review comments inline flagging cleanup opportunities
plus a couple of architectural/tech-debt items.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

https://claude.ai/code/session_01TxCfinXq7abSrbF7aTw2cA

---
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---------

Co-authored-by: Claude <noreply@anthropic.com>

packages/twenty-client-sdk/src/metadata/generated/schema.graphql

@@ -1610,6 +1610,11 @@ type BillingPlan {
   meteredProducts: [BillingMeteredProduct!]!
 }
 
+type BillingPaymentIntent {
+  clientSecret: String!
+  paymentIntentType: String!
+}
+
 type BillingSession {
   url: String
 }
@@ -1879,6 +1884,7 @@ enum ModelFamily {
 type Billing {
   isBillingEnabled: Boolean!
   billingUrl: String
+  stripePublishableKey: String
   trialPeriods: [BillingTrialPeriod!]!
 }
 
@@ -3286,6 +3292,7 @@ type Mutation {
   skipBookOnboardingStep: OnboardingStepSuccess!
   updateOneApplicationVariable(key: String!, value: String!, applicationId: UUID!): Boolean!
   checkoutSession(recurringInterval: SubscriptionInterval!, plan: BillingPlanKey! = PRO, requirePaymentMethod: Boolean! = true, successUrlPath: String): BillingSession!
+  createSubscriptionPaymentIntent(recurringInterval: SubscriptionInterval!, plan: BillingPlanKey! = PRO, requirePaymentMethod: Boolean! = true, successUrlPath: String, idempotencyKey: String!): BillingPaymentIntent!
   switchSubscriptionInterval: BillingUpdate!
   switchBillingPlan: BillingUpdate!
   cancelSwitchBillingPlan: BillingUpdate!

packages/twenty-client-sdk/src/metadata/generated/schema.ts

@@ -1258,6 +1258,12 @@ export interface BillingPlan {
     __typename: 'BillingPlan'
 }
 
+export interface BillingPaymentIntent {
+    clientSecret: Scalars['String']
+    paymentIntentType: Scalars['String']
+    __typename: 'BillingPaymentIntent'
+}
+
 export interface BillingSession {
     url?: Scalars['String']
     __typename: 'BillingSession'
@@ -1504,6 +1510,7 @@ export type ModelFamily = 'GPT' | 'CLAUDE' | 'GEMINI' | 'MISTRAL' | 'GROK'
 export interface Billing {
     isBillingEnabled: Scalars['Boolean']
     billingUrl?: Scalars['String']
+    stripePublishableKey?: Scalars['String']
     trialPeriods: BillingTrialPeriod[]
     __typename: 'Billing'
 }
@@ -2804,6 +2811,7 @@ export interface Mutation {
     skipBookOnboardingStep: OnboardingStepSuccess
     updateOneApplicationVariable: Scalars['Boolean']
     checkoutSession: BillingSession
+    createSubscriptionPaymentIntent: BillingPaymentIntent
     switchSubscriptionInterval: BillingUpdate
     switchBillingPlan: BillingUpdate
     cancelSwitchBillingPlan: BillingUpdate
@@ -4298,6 +4306,13 @@ export interface BillingPlanGenqlSelection{
     __scalar?: boolean | number
 }
 
+export interface BillingPaymentIntentGenqlSelection{
+    clientSecret?: boolean | number
+    paymentIntentType?: boolean | number
+    __typename?: boolean | number
+    __scalar?: boolean | number
+}
+
 export interface BillingSessionGenqlSelection{
     url?: boolean | number
     __typename?: boolean | number
@@ -4547,6 +4562,7 @@ export interface ClientAiModelConfigGenqlSelection{
 export interface BillingGenqlSelection{
     isBillingEnabled?: boolean | number
     billingUrl?: boolean | number
+    stripePublishableKey?: boolean | number
     trialPeriods?: BillingTrialPeriodGenqlSelection
     __typename?: boolean | number
     __scalar?: boolean | number
@@ -5978,6 +5994,7 @@ export interface MutationGenqlSelection{
     skipBookOnboardingStep?: OnboardingStepSuccessGenqlSelection
     updateOneApplicationVariable?: { __args: {key: Scalars['String'], value: Scalars['String'], applicationId: Scalars['UUID']} }
     checkoutSession?: (BillingSessionGenqlSelection & { __args: {recurringInterval: SubscriptionInterval, plan: BillingPlanKey, requirePaymentMethod: Scalars['Boolean'], successUrlPath?: (Scalars['String'] | null)} })
+    createSubscriptionPaymentIntent?: (BillingPaymentIntentGenqlSelection & { __args: {recurringInterval: SubscriptionInterval, plan: BillingPlanKey, requirePaymentMethod: Scalars['Boolean'], successUrlPath?: (Scalars['String'] | null), idempotencyKey: Scalars['String']} })
     switchSubscriptionInterval?: BillingUpdateGenqlSelection
     switchBillingPlan?: BillingUpdateGenqlSelection
     cancelSwitchBillingPlan?: BillingUpdateGenqlSelection
@@ -7321,6 +7338,14 @@ export interface LogicFunctionLogsInput {applicationId?: (Scalars['UUID'] | null
     
 
 
+    const BillingPaymentIntent_possibleTypes: string[] = ['BillingPaymentIntent']
+    export const isBillingPaymentIntent = (obj?: { __typename?: any } | null): obj is BillingPaymentIntent => {
+      if (!obj?.__typename) throw new Error('__typename is missing in "isBillingPaymentIntent"')
+      return BillingPaymentIntent_possibleTypes.includes(obj.__typename)
+    }
+    
+
+
     const BillingSession_possibleTypes: string[] = ['BillingSession']
     export const isBillingSession = (obj?: { __typename?: any } | null): obj is BillingSession => {
       if (!obj?.__typename) throw new Error('__typename is missing in "isBillingSession"')